Temperature-dependent equilibrium measurements

Binding energies for all first-row clusters [M(H2>J (n= 1-6) and several small-molecule analogues have been determined by temperature-dependent equilibrium measurements of mass-selected M ions reacting with Hj or by... 

Magnesium anthracene Ci4HioMg(THF)3 (118) can be prepared in high yield from the reaction of metallic magnesium and anthracene in THE (equation 12) . Kinetic measurements showed that a reversible temperature-dependent equilibrium exists between anthracene, magnesium and 118, the latter being favored at lower temperatures. This equilibrium opened a way to the preparation of elemental magnesium in a finely dispersed. 

K s , is correspondingly higher than in the doped material. Some relaxation data are shown in Fig. 6.9 and the general similarity to the data in Fig. 6.3 is obvious. The activation energy is nearly 1.5 eV, again consistent with Eq. (6.4). The temperature-dependent equilibrium defect density has been observed by ESR, PDS and by photoconductivity measurements (McMahon and Tsu 1987, Xu et al. 1988). Some ESR data have found the opposite behavior, in which the defect density is reduced after a rapid quench and relaxes to a higher value... 

Finally, the rate of response of a coated sensor is temperature dependent. When measurements are made under conditions of equilibrium between free and sorbed analyte, changes in kinetics present no problem unless the response becomes too slow for a chosen application. In some cases, however, the rate of response can be used to identify the species being detected an example is the molecular size-dependent diffusion of organic solvents into some polymer films [35]. In this case, failure to accurately measure and/or control temperature could lead to misidentification of the analyte. 

The thermodynantic driving force (AG) for each of the S-state transitions has been estimated from measurements of the temperature-dependent equilibrium constants for the fight-induced transient intermediate states P680+/Yz and Yz /WOC(Mn). These values were then placed on... 

With t-jump, the temperature of a sample is rapidly changed. Thus, any temperature-dependent equilibrium is perturbed and the concentrations of reactants and products must be altered to the values necessary for equilibrium at the new temperature. If the temperature change is more rapid than the system can react, then the relaxation of the concentration alterations can be measured. This time dependence, which is usually exponential, can then be utilized to derive rate constants at the final temperature for the involved chemical reactions (Turner, 1986). 

From measurements of the dielectric constant of liquid sulfur in the temperature range 134-206 °C [15] it was concluded that the molar polarization increases from 134-159 °C which was explained by the assumption of a temperature dependent equilibrium between Ss(crown) and Ss(chair) molecules, the latter possessing a permanent dipole moment owing to their low symmetry (Cs). However, the most natural rationalization of the findings is that certain components of r-sulfur like Sy and Sg—molecules of low symmetry possessing a dipole moment—contribute to the molar polarization. Since their concentration increases with temperature up to the polymerization transition it is to be expected that the molar polarization changes accordingly. Above 159 °C the molar polarization is proportional to the polymer content of the melt. 

At equilibrium conditions the Gibbs energy expression 2.8 equals to zero and allows one to define the equilibrium state in terms of the measurable temperature-dependent equilibrium constant K q,... 

Gas-phase metal-ligand bond energies can be measured by a variety of experimental techniques. Measurements of absolute values can be made by temperature-dependent equilibrium methods, " " blackbody infrared radiative dissociation (BIRD), " radiative association, " and the TCID method discussed in detail here. Measurements of relative thermochemistry can be accomplished using equilibrium methods, the kinetic method, " and competitive CID (see Section 2.12.5.7). This review cannot include the details of all such measurements. 

Unfortunately, many commonly used methods for parameter estimation give only estimates for the parameters and no measures of their uncertainty. This is usually accomplished by calculation of the dependent variable at each experimental point, summation of the squared differences between the calculated and measured values, and adjustment of parameters to minimize this sum. Such methods routinely ignore errors in the measured independent variables. For example, in vapor-liquid equilibrium data reduction, errors in the liquid-phase mole fraction and temperature measurements are often assumed to be absent. The total pressure is calculated as a function of the estimated parameters, the measured temperature, and the measured liquid-phase mole fraction. 

Enthalpy changes for biochemical processes can be determined experimentally by measuring the heat absorbed (or given off) by the process in a calorimeter (Figure 3.2). Alternatively, for any process B at equilibrium, the standard-state enthalpy change for the process can be determined from the temperature dependence of the equilibrium constant ... 

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

The AS6 may be obtained from equilibrium measurements of the free energy and its dependence upon temperature, or more directly, by measuring the ACP(T) of a solution of frozen-in atomic configuration. The AQP at any one temperature is the... 

The temperature dependence of the equilibrium cell voltage forms the basis for determining the thermodynamic variables AG, A//, and AS. The values of the equilibrium cell voltage A%, and the temperature coefficient dA< 00/d7 which are necessary for the calculation, can be measured exactly in experiments. 

Equilibrium vapor pressures were measured in this study by means of a mass spectrometer/target collection apparatus. Analysis of the temperature dependence of the pressure of each intermetallic yielded heats and entropies of sublimation. Combination of these measured values with corresponding parameters for sublimation of elemental Pu enabled calculation of thermodynamic properties of formation of each condensed phase. Previ ly reported results on the subornation of the PuRu phase and the Pu-Pt and Pu-Ru systems are correlated with current research on the PuOs and Pulr compounds. Thermodynamic properties determined for these Pu-intermetallics are compared to analogous parameters of other actinide compounds in order to establish bonding trends and to test theoretical predictions. 

Rodebush has also implied that the accuracy with which very low temperatures can be measured is restricted by the uncertainty principle and by the nature of the substance under investigation. However, the accuracy of a temperature measurement is not limited in a serious way by the uncertainty principle for energy, inasmuch as the relation between the uncertainty in temperature and the length of time involved in the measurement depends on the size of the thermometer, and the uncertainty in temperature can be made arbitrarily small by sufficiently increasing the size of the thermometer we assume as the temperature of the substance the temperature of the surrounding thermostat with which it is in either stable or metastable equilibrium, provided that thermal equilibrium effective for the time of the investigation is reached. 

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